What was the role played by nuclear weapons in the Korean War?

Korea was the FIRST "Limited War" (Vietnam was the SECOND) fought during the Cold War. Nuclear Weapons created the Cold War. A "Limited War" was fought with "limitations" on where the war would be fought and using only conventional weapons. Without Nuclear Weapons, the US/Allies would have probably invaded Red China, when Communist China entered the war. Which of course would have caused the Soviet Union to enter the war. Which naturally would have led to WW3. The Soviets tested their first Atomic Weapon in 1949.